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ICSE Class 10 Physics Question 18 of 20

Solved 2017 Question Paper ICSE Class 10 Physics — Question 12

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Question

Question 8(c)

(i) A wire of length 80 cm has a frequency of 256 Hz. Calculate the length of a similar wire under similar tension, which will have frequency 1024 Hz. [4]

(ii) A certain sound has a frequency of 256 hertz and a wavelength of 1.3 m.

  1. Calculate the speed with which this sound travels.

  2. What difference would be felt by a listener between the above sound and another sound travelling at the same speed, but of wavelength 2.6 m?

Answer

(i) Given,

l1 = 80 cm, f1 = 256 Hz, f2 = 1024 Hz, l2 = ?

Since, f ∝ 1l\dfrac{1}{l}

Therefore, f1l1 = f2l2

or

f2=f1l1f2=256×801024=20 cmf_2 = \dfrac{f_1l_1}{f_2} \\[0.5em] = \dfrac{256 \times 80}{1024} \\[0.5em] = 20 \text{ cm}

(ii) Given, f = 256 Hz, λ = 1.3 m

(a) V = fλ = 256 x 1.3 = 332.8 m s-1

(b) Speed of second sound (V') = 332.8 m s-1

Wavelength of second sound (λ') = 2.6 m

f=V′λ′=332.82.6=128 Hz\text{f} = \dfrac{V'}{λ'} \\[0.5em] = \dfrac{332.8}{2.6} \\[0.5em] = 128 \text{ Hz}

As frequency of second sound is less as compared to the first sound, hence, to the listener, the first sound of wavelength 1.3 m will appear to be shriller than the second sound of wavelength 2.6 m.