QUESTION 4 In the diagram, a vehicle with a siren attached to its roof is travelling to the right. The siren
emits a continuous note of frequency 450 Hz. Upon listening to a recording on the tape
recorder, the siren appeared to be emitting 2 sounds of different frequencies, 464 Hz and
437 Hz.
towards and
away
Emitted sound
Tape Recorder
4.1 Name the phenomenon which would have led to the recording of the two
different notes.
(1)
4.2 State and very briefly describe one useful application of this phenomenon
(as it applies to sound or light).
(3)
4.3 Use the information in the text to determine the magnitude of the velocity
at which the vehicle was travelling.
Take the speed of sound to be 340 m. s.
(4)
4.4.
Explain (in terms of the wave fronts being produced) why the observed frequencies
are respectively higher and lower than the frequency of the source. (4)

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒