Page 47 - Q & A STPM 2022 Physics

Physics Semester 3 STPM Chapter 21 Sound Waves
Answer
(i)

L
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T
(ii) Speed of transverse wave, v =
μ
λ
(iii) Length of string L = , λ = 2L
2
λ
Fundamental frequency, f = = 1 T
2 2L μ
(iv) f = 1 T
2L μ
1 2T
(I) When tension is 2T, fundamental frequency = = 2f
2L μ
1 1 2T
(II) When the length is L, fundamental frequency = = 2f
2 L μ
2  
2
Question 13
Two strings P and Q on a piano have fundamental frequencies of 262 Hz and
440 Hz respectively.
(a) The strings have the same mass per unit length m but the length of string
P is only 64% of the string Q. Determine the ratio of tensions in the two
strings.
(b) Another string R is of the same material as strings P and Q, but its diameter
is 150% of string Q, and its length is 120% of Q. Strings R and Q have the
same tension. What is the fundamental frequency of string R?

Answer
(a) The fundamental frequencies of the two strings are
f P = 1 T P and f Q = 1 T Q (L P = 0.64L Q )
2L P m 2L Q m

f P = 1 T P
f Q 0.64 T Q

T P = (0.64) 2  262 2 Semester
T Q 440
= 0.145
3

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021 STPM Q&A Physics T3.indd 407 17/02/2022 10:24 AM