A car is moving towards a high cliff. The car driver sounds a horn of frequency $$f$$. The reflected sound heard by the driver has a frequency $$2 f$$. If $$v$$ be the velocity of sound, then the velocity of the car in the same velocity units, will be

A string vibrates with a frequency of $$200 \mathrm{~Hz}$$. When its length is doubled and tension is altered, it begins to vibrate with a frequency of $$300 \mathrm{~Hz}$$. The ratio of the new tension to the original tension is

Two open organ pipes A and B of length $$22 \mathrm{~cm}$$ and $$22.5 \mathrm{~cm}$$ respectively produce 2 beats per sec when sounded together. The frequency of the shorter pipe is

A bat emitting an ultrasonic wave of frequency 4.5 $$\times$$ 10⁴ Hz at speed of 6 m/s between two parallel walls. The two frequencies heard by the bat will be