More practice questions

4. Q4. The tension in a string is made four times larger. What happens to the speed of transverse waves on it?

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   v = √(T/μ) ∝ √T, so the speed doubles.

5. Q5. A 686 Hz sound passes from air (343 m s^⁻¹) into water (1482 m s^⁻¹). Find its wavelength in each. What stays the same?

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   In air λ = 343/686 = 0.5 m; in water λ = 1482/686, about 2.16 m. The frequency, set by the source, stays the same; the speed and wavelength change.

6. Q6. Using v = √(γRT/M), estimate the speed of sound in helium at 0 °C (γ = 5/3, M = 4.0 × 10^⁻³ kg mol^⁻¹, R = 8.314 J mol^⁻¹ K^⁻¹) and compare it with NCERT Table 14.1.

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   v = √(1.667 × 8.314 × 273/0.0040), about 973 m s^⁻¹, within about 1% of the 965 m s^⁻¹ in the table.