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## Homework Statement

Consider two parallel walls perfectly reflective placed at the distance ##d = 0.8 m ##. A ball, provided with a device through which are emitted continuously frequency sound waves equal to ##f_0=430 Hz##, is launched from one wall to another. It moves with constant velocity ##v##. After some time, an observer placed at the position where the ball was thrown a beat frequency equal to ##5 Hz##.

Compute:

a) the speed of the ball;

b) assuming the formation of standing waves when the two walls are made the same traveling conditions (nodes) of the gas particles, determine the speed at which must travel the ball so that between the two walls standing waves will be generated with frequency equal to twice the fundamental frequency. Neglect, in this calculation, the higher frequency sound wave presence.

Assume the speed of sound ##c = 340 m / s##.

[Results: a) ## v = 1.98 m / s ##; b) ## v = 4 m / s ##]

## Homework Equations

Doppler effect : $$f^*=f_0(\frac{c}{c\pm v_{ball}})$$

## The Attempt at a Solution

**a.**I get confused because the result is correct if I use

$$f_{beats}=|f_0(\frac{c}{c- v_{ball}})-f_0(\frac{c}{c+v_{ball}})|$$

But this does not seem correct to me. Immediately after the first bounce the ball i moving towards the observer, so it should be

$$f_{beats}=|f_0(\frac{c}{c- v_{ball}})-f_0(\frac{c}{c-v_{ball}})|=0$$

Which of course is not.

**b**. This is the point I cannot do at all. What is the strategy to use here?

Any help is really appreciated.