6
Question 1 (20 marks)
A subwoofer loudspeaker consists of a rigid cone of mass m supported by a spring-like suspension
system with a spring constant k. In order to design a speaker box, we need to measure both m and
k. This is done by first measuring the resonant frequency, f0, of the speaker.
Next, a small piece of Blu Tack (or plasticine) of known mass m1 is attached rigidly to the cone.
The new resonant frequency, f1, is then measured.
(a) Do you expect f1 to be greater or less than f0? Explain your reasoning.
(b) Write an expression for the mass of the speaker cone, m, in terms of the measured quantities
f0, f1 and m1.
(c) Write an expression for the spring constant, k, in terms of these same measured quantities.
(d) The subwoofer is subsequently installed in its well-designed speaker box, and is found to
reproduce sounds down to 20 Hz. What is the minimum length that an organ pipe would
need to be to produce this frequency? Assume the organ pipe is open at one end and closed
at the other.
(e) Would your answer to (d) change if the organ pipe were open at both ends? Explain your
answer.
Question 2 (20 marks)
A trumpet player stands in a field and plays a note at 440 Hz. A steady wind of 20 ms-1 is blowing.
(a) What frequency is heard by a listener who is standing 5 metres downwind of the trumpeter?
(b) The listener straps on roller-skates and finds themselves carried downwind at a steady
15 ms-1. What frequency do they hear now?
(c) If the listener was initially experiencing a sound level of 86 dB from the trumpet, and the
wind creates an ambient sound level of 40 dB, how long after the listener starts moving will
it be before the trumpet is no longer audible? Explain your reasoning and any assumptions
made.
[Note: take the speed of sound to be 343 ms-1]
