Oscillations and Waves
- The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L metre long. The length of the open pipe will be Answer: 1. 2L Compare the frequencies using v as the speed of sound. Open pipe of length l : harmonics nv/2l ; the second overtone is the 3r... 1
- An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tuning fork is : Answer: 3. 150 cm Key idea: a closed pipe resonates at odd multiples of λ/4 : lengths L, 3L, 5L,dots Smallest length =λ/4=50 cm. The next re... 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