Question

1. (a) Bob Dylan plays a note of frequency f=450Hz on a harmonica while riding his bicycle towards a stationary observer. If Bob is traveling at 4m/s relative to the observer, what frequency does the observer hear?

(b) The observer plays a note of frequency f=450Hz on her harmonica wile Bob is riding towards her (Bob continues to play his harmonica as in part a). What beat frequency will the observer perceive when she hears the resulting combination of the two harmonica notes?

(c) What does the combination of harmonica notes sound like to the observer?

Answer 1

a) This problem can be interpreted as a source of sound moving towards an observer with velocity 4m/s. The frequency of the source at rest is 450Hz. So now let us use the Doppler effect equation to calculate the frequency heard by the observer.

Here f' is the frequency heard by the observer,f is the frequency emitted by the source=450Hz ,V is the speed of the source=4m/s and C is the speed of the sound wave=343m/s

So let us plug in the values.

So the observer will hear a sound of frequency 455Hz.

b) on this case, the observer is playing a harmonica at the same frequency as Bob Dylan at rest i.e.450Hz. . But she wil hear the frequency of 450Hz because Bob Dylan is moving towards her. So for her, the two frequencies that superpose to form beats are 455 Hz and 450Hz.

Beat frequency of two superimposing waves which differ slightly in frequency is just the difference between these frequencies. Therefore the beat frequency=450-400=5Hz.

c) the beat frequency is 5Hz. So the observer hears 5 beats of harmonica per second. This means, the sound of the combination of two harmonicas is heard with the frequency of 5Hz. So to the observer,notes sound like they are vanishing 5 times in each second.