Question

In this problem take the speed of sound to be 343 m/s. How fast, in meters per second, does an observer need to approach a stationary sound source in order to observe a 1.4 % increase in the emitted frequency?

Answer 1

To observe a 1.4% increase in frequency due to the Doppler Effect, the observer needs to approach a stationary sound source at approximately 4.8 meters per second.

Step-by-step explanation:

The phenomenon being described is the Doppler Effect, which occurs when a sound source and an observer are moving relative to each other, resulting in a change in the observed frequency of sound. To calculate the observer's required speed for a 1.4% increase in the emitted frequency, we can use the Doppler Effect equation for sound:

f' = f (v + vo) / (v + vs)

Where f' is the observed frequency, f is the emitted frequency, v is the speed of sound, vo is the observer's speed toward the source, and vs is the source's speed relative to the medium (zero in this case since the source is stationary).

We know the observed frequency is 1.4% higher than the emitted frequency, so:

1.014f = f (343 + vo) / 343

By rearranging the equation and solving for vo, we get:

vo = 343 (1.014 - 1)

vo = 4.802 m/s

Therefore, the observer needs to approach the stationary sound source at a speed of approximately 4.8 meters per second to observe a 1.4% increase in the emitted frequency due to the Doppler Effect.