# Mike is playing his speaker at an unknown frequency. His friend, Emma, gets on her bike and rides away from Mike at a uniform speed, holding an open-air column horizontally over her head. What was the frequency of the sound coming from Mike's speaker?

##
Mike is playing his speaker at an unknown frequency on a hot #31.0^@C# day. His friend, Emma, gets on her electric bike and rides away from Mike with a uniform speed of #16.0m/s# , holding a #0.450m# open-air column horizontally over her head. The air rushing through the tube produces a third harmonic tone in the tube. Mike hears a beat frequency of #5.00Hz# . What was the frequency of the sound coming out of Mike's speaker?

Mike is playing his speaker at an unknown frequency on a hot

(significant figures excluded)

Order of Solving

Using the formula, the speed of the sound waves coming from Mike's speaker was

Step 2 The air travelling from Mike's speaker through the tube above Emma's head produces a third harmonic tone. Since the information regarding the tube's length and harmonic is given, we can use that knowledge to combine it with the speed of the sound waves to determine the frequency of the sound coming from the tube. This can be found by using the formula for the frequency of standing waves in an air column open at both ends:

Step 3 The Doppler effect causes a change in the frequency heard by Mike as Emma rides away from him. The frequency that he hears is lower than the actual frequency of the sound waves in the tube. To derive the frequency detected by Mike, we can use the Doppler effect formula for sound:

Since the equation has an absolute value sign, there are two possible scenarios.

By signing up, you agree to our Terms of Service and Privacy Policy

The frequency of the sound coming from Mike's speaker would decrease as Emma rides away from him due to the Doppler effect. If ( f ) is the frequency emitted by Mike's speaker, ( f' ) is the frequency heard by Emma, ( v ) is the speed of sound, and ( v_{\text{b}} ) is the speed of Emma's bike, then the Doppler effect equation for sound moving away from the observer is:

[ f' = \frac{v}{v - v_{\text{b}}} \times f ]

Given the open-air column held horizontally, the sound waves would be traveling in the same direction as Emma's motion. Thus, ( v_{\text{b}} ) is negative. The equation becomes:

[ f' = \frac{v}{v + v_{\text{b}}} \times f ]

Emma's speed ( v_{\text{b}} ) would be relevant to compute the frequency observed by Emma. Without the specific values of ( v ) and ( v_{\text{b}} ), the exact frequency cannot be determined.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- One of the strings of a guitar has a fundamental frequency of 440 Hz and another has a fundamental frequency of 660 Hz. Which of the following set of frequencies could be produced on both of these strings?
- Why are sound waves in air characterized as longitudinal?
- Word Problem regarding The Doppler Effect?
- How are harmonics generated in a transformer?
- How is the doppler effect used in an ultrasonography diagnostic?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7