AP Physics 1 : Waves
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Example Questions
Example Question #1 : Sound Waves
Alice measures the wavelength and frequency of a sound wave as
At what speed is the sound traveling?
We know from the question that
Frequency is the inverse of period:
The velocity of a wave is its wavelength multiplied by its frequency:
Example Question #1 : Waves
You are standing on the sidewalk when a police car approaches you at 
The doppler effect follows this formula:
In this equation, 
Plugging the given values in, we can describe the initial situation as:
Note that the velocity is negative 
Therefore,
When the police car is driving away, the situation is described with a positive velocity:
Therefore,
Example Question #1 : Sound Waves
A guitar player uses beats to tune his instrument by playing two strings. If one vibrates at 550 Hz and the second at 555 Hz, how many beats will he hear per minute?
Two waves will emit a beat with a fequency equal to the difference in frequency of the two waves. In this case the beat frequency is:
Convert to beats per minute:
Example Question #1 : Waves
The ukulele is a short instrument, relative to a guitar. How does this affect the frequencies of sounds that these two instruments produce? Assume the two instruments use the same strings.
The shorter length strings produce lower frequencies
The shorter length strings produce higher frequencies
The shorter length creates a lower speed of sound
The shorter length creates a higher speed of sound
The shorter length strings produce higher frequencies
The speed of sound in air is constant, assuming that the temperature of the air is constant. When the length of the string is shortened, by the principles of standing waves, this creates a higher frequencies. Assuming that the two instruments use the same strings is equivalent to stating that the two instruments have strings of equal linear mass density. This situation represents a standing wave, thus we can relate the following equation for the first harmonic:
Where, 
Since the velocity of sound in a fixed medium is constant, we see that a shorter length, 
Example Question #1 : Waves
A sound played from a speaker is heard at an intensity of 100W from a distance of 5m. When the distance from the speaker is doubled, what intensity sound will be heard?
Intensity is related to radius by the inverse square law:
This equation is derived from the concept that the energy from the sound waves is conserved and spread out over an area, producing the 
Example Question #4 : Waves
A stopped pipe (closed at both ends) sounds a frequency of 500Hz at its fundamental frequency. What is the length of the pipe?
Rearrange the equation to solve for L, then plug in given values and solve.
Example Question #1 : Waves
What is the beat frequency between a 305Hz and a 307Hz sound?
Frequency of beats is determined by the absolute value of the difference between two different frequencies. Thus, the beats frequency is 2Hz. Note that beat frequency is always a positive number.
Example Question #2 : Waves
An open pipe (open at both ends) has a fundamental frequency of 600Hz. How long is the pipe?
An open pipe can be modeled by the following equation:
Rearrange the equation to solve for 
Example Question #3 : Waves
A student at a concert notices that a balloon near the large speakers moving slightly towards, then away from the speaker during the low-frequency passages. The student explains this phenomenon by noting that the waves of sound in air are __________ waves.
longitudinal
torsional
electromagnetic
transverse
latitudinal
longitudinal
Sound is a longitudinal, or compression wave. A region of slightly more compressed air is followed by a region of slightly less compressed air (called a rarefaction). When the compressed air is behind the balloon, it pushes it forward, and when it is in front of the balloon, it pushes it back. This only works if the frequency is low, because the waves are long enough so that the balloon can react to them.
Example Question #8 : Waves
Consider a 37cm long harp string with a fundamental frequency of 440Hz.
Calculate the speed of the standing wave created by plucking this string.
Use the following equation to find the velocity of the wave, using its fundamental frequency and the length:
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