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NCERT Solutions · Class 9 Science Sound Waves: Characteristics and Applications

28 questions · 16 still being checked

Revise, Reflect, Refine 10.14–10.15 (part 21 of 21)

  1. Exercise 10.14

    The graphical representation of two sound waves A and B propagating at the same speed of 345\displaystyle 345 m s−1\displaystyle s^{-1} is shown in Fig. 10.33. What is the wavelength of each of them? Also, calculate their frequencies. DensityNCERT_Question_Class9_Science_Ch10_RRR_Q10-14
    NCERT’s answer
    0.$\displaystyle 025$ m, $\displaystyle 0.05$ m; $\displaystyle 13800$ Hz, $\displaystyle 6900$ Hz
    Wave A: \(\displaystyle \lambda_A = 0.025\ \text{m} \), \(\displaystyle \nu_A = 13800\ \text{Hz} \). Wave B: \(\displaystyle \lambda_B = 0.05\ \text{m} \), \(\displaystyle \nu_B = 6900\ \text{Hz} \).
    Read each wavelength crest-to-consecutive-crest off the shared distance axis of Fig. $\displaystyle 10.33$: A repeats every \(\displaystyle 2.5\ \text{cm} = 0.025\ \text{m} \), B every \(\displaystyle 5.0\ \text{cm} = 0.05\ \text{m} \).
    \(\displaystyle \nu_A = \dfrac{v}{\lambda_A} = \dfrac{345\ \text{m s}^{-1}}{0.025\ \text{m}} = 13800\ \text{Hz} \).
    \(\displaystyle \nu_B = \dfrac{v}{\lambda_B} = \dfrac{345\ \text{m s}^{-1}}{0.05\ \text{m}} = 6900\ \text{Hz} \).
    B's wavelength is exactly twice A's, so its frequency is exactly half — the two share one speed, as \(\displaystyle v = \nu \lambda \) requires.

  2. Exercise 10.15

    Two identical sound sources are placed at A and B — one in air and one submerged in water (Fig. 10.34\displaystyle 10.34). Both produce sounds at the same time, which travel horizontally to the vertical side of the cliff and come back. If the time taken by the sound to return to A is 4.5\displaystyle 4.5 times than that of B, what is the ratio between the speeds of sound in air and water?NCERT_Question_Class9_Science_Ch10_RRR_Q10-15
    NCERT’s answer
    $\displaystyle 2$:$\displaystyle 9$
    \(\displaystyle v_{\text{air}} : v_{\text{water}} = 2 : 9 \).
    Both sources sit the same horizontal distance \(\displaystyle d \) from the cliff face, and each sound travels there and back, covering \(\displaystyle 2d \).
    Times to return: \(\displaystyle t_A = \dfrac{2d}{v_{\text{air}}} \) and \(\displaystyle t_B = \dfrac{2d}{v_{\text{water}}} \).
    Given \(\displaystyle t_A = 4.5\, t_B \): \(\displaystyle \dfrac{2d}{v_{\text{air}}} = 4.5 \times \dfrac{2d}{v_{\text{water}}} \), and \(\displaystyle 2d \) cancels from both sides.
    \(\displaystyle \dfrac{1}{v_{\text{air}}} = \dfrac{4.5}{v_{\text{water}}} \Rightarrow \dfrac{v_{\text{air}}}{v_{\text{water}}} = \dfrac{1}{4.5} = \dfrac{2}{9} \).
    So sound is $\displaystyle 4.5$ times faster in water than in air — matching the chapter's statement that sound travels about $\displaystyle 4$–$\displaystyle 5$ times faster in water.