Page 50 - Q & A STPM 2022 Physics

Physics Semester 3 STPM Chapter 21 Sound Waves
Question 15

(a) A string is stretched between two fixed points. The mid point of the string
is plucked and then released. Explain how a standing wave is set up in the
string.
Draw the fundamental mode of vibration of the standing wave.
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(b) A string fixed at both ends and having a mass of 4.80 g, a length of 2.00 m,
and a tension of 48.0 N vibrates in its second mode (n = 2).
(i) What is the ratio of the wavelength in air of the sound emitted by this
vibrating string and the wavelength of the wave in the string?
(ii) Find the three lowest frequencies of standing waves in the string?
(Speed of sound in air = 330 m s )
–1

Answer
(a) After the string is plucked and released, pulses of wave travel along the
string toward the two fixed ends of the string where the wave pulses are
repeatedly reflected. Superposition of the reflected waves travelling in
opposite directions along the string produces the standing wave.

Fundamental mode

(b)

L

(i) Wavelength in string, λ = L = 2.00 m
2 T
Frequency of sound, f =
2L μ
v
Wavelength of sound wave, λ sound = (v = speed of sound)
f
μ
= vL T
(4.80 × 10 /2.00)
–3
= (330)(2.00) m
48.0
= 4.67 m
Wavelength of sound 4.67
= = 2.34
Wavelength in string 2.00
Semester
3

410

021 STPM Q&A Physics T3.indd 410 17/02/2022 10:24 AM