Question

Brody, The dog, is sitting at your feet like a good boy. You throw a dog toy away from you at a speed of 34 m/s (assume constant horizontal velocity). Brody runs after the ball at a constant speed of 7 m/s. The toy is designed to make a constant high frequency tone of 950 Hz as it flies through the air.What frequency do you hear the toy make?

Answer 1

Answer: 1054.53 Hz

Explanation: this is a question under the principle of Doppler effect .

Doppler effect is a mathematical statement that gives the value of the observed frequency by an observer when there is a relative motion between the observer and the source of sound.

This is mathematically given as

fo = (v + vo)/(v - vs) × f

Where fo = observed frequency =?

v = speed of sound in air = 343 m/s

vo = velocity of observer = 0 ( since I am at rest )

vs = velocity of the source of sound ( in this case the dog toy ) = 34m/s....this value is positive because it is moving away from the observer.

f = frequency of sound produced by source = 950 Hz

By substituting the parameters, we have that

fo = (343+0)/(343-34) × 950

fo = (343/ 309) × 950

fo = 1.11 × 950 = 1054.53 Hz