Question

Two motorcycles are traveling in opposite directions at the same speed when one of the cyclists blasts her horn, which has frequency of 544 Hz. The other cyclist hears the frequency as 563 Hz. If the speed of sound in air is 344 m/s, what is the speed of the motorcycles

Answer 1

The speed of the motorcycles is 29 m/s.

Step-by-step explanation:

To determine the speed of the motorcycles, we can use the Doppler effect formula for sound. The formula is:

Δf = (v - vs) / v * f

where Δf is the change in frequency, v is the speed of sound in air, vs is the speed of the source (motorcycle) relative to the medium (air), and f is the frequency of the sound emitted by the source.

In this case, the change in frequency is 563 Hz - 544 Hz = 19 Hz, the speed of sound is 344 m/s, and the frequency emitted is 544 Hz. Plugging these values into the formula, we get:

19 Hz = (344 m/s - vs) / 344 m/s * 544 Hz

Simplifying the equation, we find that the speed of the motorcycles, vs, is 29 m/s.

Answer 2

6ms^-1

Step-by-step explanation:

Given that the frequency difference is

( 563- 544) = 19

So alsoThe wavelength of each wave is = v/f = 344 /544

and there are 19 of this waves

So it is assumed that each motorcycle has moved 0.5 of this distance

in one second thus the speed of the motorcycles will be

=> 19/2 x 344/544 = 6.0 m/s