Waves - Detailed Help

Assignment WM3: Speed of a Wave

Objectives:
  • The student should be able to define wave speed and identify the variables which effect wave speed.
  • The student should be able to utilize the definition of wave speed to solve simple computational problems involving speed, distance and time.

 

Reading:

The Physics Classroom, Waves Unit, Lesson 2, Part d

 

 

The speed of a wave is DEFINED as _____.


Definition of Wave Speed:

The wave speed refers to the distance traveled by a point on the wave pattern per unit of time. It is often measured in units such as meters/second and describes how fast the wave is moving through the medium.


There are numerous ways to calculate the speed of a wave. But don't be fooled! The definition of a physics quantity is not the same thing as the formula used to calculate the quantity. While wave speed can be calculated as the wavelength multiplied by the frequency, this is not the way it is defined. See Define Help section above.


How is the speed of a wave defined?

 

 

If a traveling wave is described as moving fast, then one can be sure that _____.


Definition of Wave Speed:

The wave speed refers to the distance traveled by a point on the wave pattern per unit of time. It is often measured in units such as meters/second and describes how fast the wave is moving through the medium.


The speed of a wave, or any object for that matter, is the distance it travels per unit of time. Speed is sometimes referred to as a measure of how fast an object is moving. A fast moving wave has a large speed. That is to say that it covers a large distance in a short amount of time compared to a slow moving wave.


How are fast waves different than slow waves?

 

 

The speed of a wave depends upon the ____. List all that apply ... .


Factors Affecting Wave Speed:

The speed of a wave is dependent upon the properties of the medium through which the wave is moving. An alteration in the properties of the medium will result in a change in the speed at which the wave moves through that medium.


The speed of a wave is often calculated as the product of frequency and wavelength. This gives many students the wrong impression that the speed of a wave depends upon frequency and wavelength. But don't be fooled! The speed of a wave is independent of its frequency and wavelength. A change in the frequency value will not result in a change in the speed value. Rather, changing frequency will result in a change in the wavelength in such a manner that the speed value turns out the same. While the speed can be calculated from knowledge of the frequency and wavelength, its value is unaffected by changes in frequency and wavelength.


What variables would effect the speed of a wave?

 

 

Which of the following would effect the speed of a water wave? That is, which could be altered and subsequently alter the wave speed? List all that apply ... .


Factors Affecting Wave Speed:

The speed of a wave is dependent upon the properties of the medium through which the wave is moving. An alteration in the properties of the medium will result in a change in the speed at which the wave moves through that medium.


The speed of a wave is often calculated as the product of frequency and wavelength. This gives many students the wrong impression that the speed of a wave depends upon frequency and wavelength. But don't be fooled! The speed of a wave is independent of its frequency and wavelength. A change in the frequency value will not result in a change in the speed value. Rather, changing frequency will result in a change in the wavelength in such a manner that the speed value turns out the same. While the speed can be calculated from knowledge of the frequency and wavelength, its value is unaffected by changes in frequency and wavelength.


It is often said that the speed of a wave depends upon the properties of the medium (see Physics Rules section above). The actual properties which matter will vary from medium to medium. For instance, the speed of a sound wave traveling through air is mostly dependent upon the temperature of the air. The speed of a transverse wave traveling through a rope or wire is dependent upon the density of the wire and the tension to which the wire is pulled. In each of these cases, it is the property of the medium which has an impact upon wave speed. Now consider this question. Of the choices listed, which is/are properties of the water?


What variables would effect the speed of a wave?

 

 

Two waves - wave A and wave B - are introduced into two slinkies having identical properties. Wave A has a frequency of 4 Hz and an amplitude of 50 cm. Wave B has a frequency of 2.5 Hz and an amplitude of 40 cm. Which wave is likely to have the greatest speed?


Factors Affecting Wave Speed:

The speed of a wave is dependent upon the properties of the medium through which the wave is moving. An alteration in the properties of the medium will result in a change in the speed at which the wave moves through that medium.

The speed of a wave is often calculated as the product of frequency and wavelength. This gives many students the wrong impression that the speed of a wave depends upon frequency and wavelength. But don't be fooled! The speed of a wave is independent of its frequency and wavelength. A change in the frequency value will not result in a change in the speed value. Rather, changing frequency will result in a change in the wavelength in such a manner that the speed value turns out the same. While the speed can be calculated from knowledge of the frequency and wavelength, its value is unaffected by changes in frequency and wavelength.


What variables would effect the speed of a wave?

For two waves of varying frequency and the same amplitude in the same medium, which would have the greatest speed?

 

 

Mac and Tosh are creating waves using a 3-inch zinc-coiled slinky. If they double the frequency of the waves which they are creating (without any alteration in the medium), then one can be sure that ____.


Factors Affecting Wave Speed:

The speed of a wave is dependent upon the properties of the medium through which the wave is moving. An alteration in the properties of the medium will result in a change in the speed at which the wave moves through that medium.


The speed of a wave is often calculated as the product of frequency and wavelength. This gives many students the wrong impression that the speed of a wave depends upon frequency and wavelength. But don't be fooled! The speed of a wave is independent of its frequency and wavelength. A change in the frequency value will not result in a change in the speed value. Rather, changing frequency will result in a change in the wavelength in such a manner that the speed value turns out the same. While the speed can be calculated from knowledge of the frequency and wavelength, its value is unaffected by changes in frequency and wavelength.


It is often said that the speed of a wave depends upon the properties of the medium (see Physics Rules section above). If the properties of the medium are not changed, the speed of the wave is not changed. Frequency and wavelength are wave properties, not properties of a slinky. You would never look at a slinky sitting on a table and say "Look at that slinky. It has a wavelength of 20 cm." Wavelength is a property of a wave. The material a slinky is made of and the size of its coils and the tightness to which it is pulled are properties of a slinky. Alterations in these properties affect the ultimate speed of the wave.


What variables would effect the speed of a wave?

How would an alteration in the frequency of a wave effect the speed of the wave?

 

 

An oceangoing vessel uses sonar to measure the depth of the ocean. If a sound wave sent from the ship bounces off the ocean floor 525.0 m below and returns to the ship after 0.875 seconds, then what is the speed (in m/s) of the sound waves in water?

(Note: Your numbers are selected at random and likely different from the numbers listed here.)


The speed of a wave refers to how fast it travels through a medium. By definition, it is the distance traveled per unit of time.

Speed = distance traveled / time of travel = d / t


It is an all too common tendency of a physics student to view physics problems as simply math exercises. For certain, physics problems will exercise your math skills. But don't be fooled! A physics problem such as this one is more than a math exercise; it is a test of your ability to read, interpret, visualize and analyze. And if you are missing this question, it is not because your math has failed you. Rather, there is a need to read more carefully, analyze the question, interpret what is happening and visualize the situation. In the short 0.875 seconds of time, the sound wave travels from ocean surface to the ocean floor 525.0 m below and then another 525.0 m back up to the ocean surface. The total distance traveled by the wave in this amount of time is 1050.0 m. Now you can do your math.


How is the speed of a wave mathematically related to the distance traveled and the time of travel?

 

 

A water wave travels through a reflecting pool which is 11.0 m long. A physics students times one complete down-and-back motion of a ripple through the pool to take 8.20 seconds. What is the speed (in m/s) of the water wave?

(Note: Your numbers are selected at random and likely different from the numbers listed here.)


The speed of a wave refers to how fast it travels through a medium. By definition, it is the distance traveled per unit of time.

Speed = distance traveled / time of travel = d / t

 


It is an all too common tendency of a physics student to view physics problems as simply math exercises. For certain, physics problems will exercise your math skills. But don't be fooled! A physics problem such as this one is more than a math exercise; it is a test of your ability to read, interpret, visualize and analyze. And if you are missing this question, it is not because your math has failed you. Rather, there is a need to read more carefully, analyze the question, interpret what is happening and visualize the situation. In the 8.20 seconds of time, the water wave travels from one end of the pool to the other end 11.0 m away and then back to the original end another 11.0 m. The total distance traveled by the water wave in this amount of time is 22.0 m. Now you can do your math.


How is the speed of a wave mathematically related to the distance traveled and the time of travel?

 

 

A sound wave having a frequency of 261 Hz is observed to travel 341.0 meters in 1.0 seconds. What is the speed (in m/s) of the sound wave?

(Note: Your numbers are selected at random and likely different from the numbers listed here.)


The speed of a wave refers to how fast it travels through a medium. By definition, it is the distance traveled per unit of time.

Speed = distance traveled / time of travel = d / t

 


It is not uncommon for a student of physics to be insistent that all the information given in a problem is required to obtain the answer. But don't be fooled! Physics problems are mostly about (or at least should be mostly about) making right choices between what is important and unimportant in a given situation. Physics problems like this one are more than plug-and-chug exercises; they are tests of whether you understand the concepts clearly.

There are three pieces of quantitative information given in this question. Only two of the pieces are of importance. Deciding on which two pieces are important demands that you understand the two equations for wave speed (see Formula Fix sections above and below). Using the equation below demands that you know both frequency and wavelength values. While the frequency is known as recognized by its characteristic unit (Hz), the wavelength is not known. The 341.0 m is the distance traveled by the wave in the 1.0 second of travel. Knowing the distance traveled and the time of travel means that the v = d /t equation should be used to determine wave speed.


The speed (v) of a wave can be calculated from knowledge of the wavelength () and the frequency (f) of the wave. The formula is:

v = f •

 


How is the speed of a wave mathematically related to the distance traveled and the time of travel?