Wave motion: longitudinal and transverse waves, wave speed
- If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is : Answer: 4. 1 : √(2) Speed of a transverse wave on a string is v=√(T/μ) , so v∝sqrt T . v_i/v_f=√(T/2T)=1/sqrt2 , i.e. 1:sqrt2 . Option (4) i... 1
- Two cars moving in opposite directions approach each other with speed of 22 m/s and 16.5 m/s respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is [velocity of sound 3… Answer: 3. 448 Hz Key idea: Doppler effect with source and observer approaching: f'=fv+v_o/v-v_s . f'=400×340+16.5/340-22=400×356.5/318≈448... 1
- A siren emitting a sound of frequency 800 Hz moves away from an observer towards a cliff at a speed of 15\ ms^-1. Then, the frequency of sound that the observer hears in the echo reflected from the cliff is : (Take velocity of sound in air = 330\ ms^… Answer: 3. 838 Hz Key idea: the cliff is a stationary reflector. The sound reaches it with a Doppler shift because the siren moves toward th... 1
- A uniform rope of length L and mass m_1 hangs vertically from a rigid support. A block of mass m_2 is attached to the free end of the rope. A transverse pulse of wavelength λ_1 is produced at the lower end of the rope. The wavelength of the pulse whe… Answer: 2. √(m₁+m₂/m₂) Key idea: the frequency of a pulse stays the same, so wavelength is proportional to wave speed v=√(T/μ) . At the lowe... 1