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Page 511: Practice Problems

Exercise 39

Step 1

1 of 3

The general formula for Doppler effect problems is

$f_{listener}=f_{source}dfrac{v_{sound}pm v_{listener}}{v_{sound}pm v_{source}}$

The rules are:

If the listener is travelling towards the source, the sign of $v_{listener}$ is positive. If it’s moving away, then it is negative.

Furthermore, if the source is moving towards from the listener, the sign of $v_{source}$ is negative. If the source is moving away from the listener, it is positive.

Step 2

2 of 3

The sign of $v_{listener}$ is positive since it is moving towards the source.

$451=440left(dfrac{343+v_{listener}}{343}right)$

Solve for $v_{listener}$

$$
v_{observer}=8.58;m/s
$$

Result

3 of 3

$$
v_{observer}=8.58;m/s
$$

Exercise 40

Step 1

1 of 3

The general formula for Doppler effect problems is

$f_{listener}=f_{source}dfrac{v_{sound}pm v_{listener}}{v_{sound}pm v_{source}}$

The rules are:

If the listener is travelling towards the source, the sign of $v_{listener}$ is positive. If it’s moving away, then it is negative.

Furthermore, if the source is moving towards from the listener, the sign of $v_{source}$ is negative. If the source is moving away from the listener, it is positive.

Step 2

2 of 3

The sign of $v_{listener}$ is positive since it is moving the toward the source.

Plug-in the given values and solve for $f_{source}$

$375=f_{source}left(dfrac{343+25}{343}right)$

Solve for $f_{source}$

$$
f_{source}=350;Hz
$$

Result

3 of 3

$$
f_{source}=350;Hz
$$

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Page 511: Practice Problems

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