Question

I NEED HELP!!!!!!!!!!!

1. A train is moving at 23 m/s due east when it sounds a blast on its horn, frequency = 164 Hz. What frequency is heard by the driver of a car moving due east at 15 m/s along a road parallel to the tracks? Use 343 m/s for the speed of sound. Please show all work.


2. A laser beam from Earth is reflected back from a mirror on the Moon in 2.60 s. If the
distance between Earth and the Moon is 3.85 × 108 m, calculate the speed of light.
Please show all work.

Answer 1

1. 168.1 Hz

To find the apparent frequency heard by the driver in the car, we can use the formula for the Doppler effect:

$f'=(\frac{v\pm v_o}{v\pm v_s})f$

where

f is the original sound of the horn

v is the speed of sound

$v_o$ is the velocity of the observer (the driver and the car), which is positive if the observer is moving towards the source and negative if it is moving away

$v_s$ is the velocity of the sound source (the train), which is positive if the source is moving away from the observer and negative otherwise

In this problem we have, according to the sign convention used:

$v = 343 m/s\\f = 164 Hz\\v_o = -15 m/s\\v_s = -23 m/s$

Substituting, we find:

$f'=(\frac{343-15}{343-23})(164)=168.1 Hz$

2.  $2.96\cdot 10^8 m/s$

The speed of light can be calculated as

$v=\frac{d}{t}$

where

d is the distance travelled

t is the time taken

In this problem:

$d=2\cdot 3.85\cdot 10^8 =7.7\cdot 10^8 m$ is the total distance travelled by the laser beam (twice the distance between the Earth and the Moon)

t = 2.60 s is the time taken

Substituting in the formula,

$v=\frac{7.7\cdot 10^8 m}{2.60 s}=2.96\cdot 10^8 m/s$