A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The string is set into vibration using an external vibrator of frequency 100 Hz. The separation between successive nodes on the string is close to -

A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is ƒ₁. If the speed of the train is reduced to 17 m/s, the frequency registered is ƒ₂. If speed of sound is 340 m/s, then the ratio ƒ₁/ƒ₂ is -

A musician using an open flute of length 50 cm producess second harmonic sound waves. A person runs towards the musician from another end of hall at a speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running person shall be close to :

A heavy ball of mass M is suspendeed from the ceiling of a car by a light string of mass m (m < < M). When the car is at rest, the speed of transverse waves in the string is 60 ms^$$-$$1. When the car has acceleration a, the wave-speed increases to 60.5 ms^$$-$$1. The value of a, in terms of gravitational acceleration g, is closest to :