A string of length $$25 \mathrm{~cm}$$ and mass $$10^{-3} \mathrm{~kg}$$ is clamped at its ends. The tension in the string is $$2.5 \mathrm{~N}$$. The identical wave pulses are generated at one end and at regular interval of time, $$\Delta \mathrm{t}$$. The minimum value of $$\Delta \mathrm{t}$$, so that a constructive interference takes place between successive pulses is

With what velocity should an observer approach a stationary sound source, so that the apparent frequency of sound should appear double the actual frequency?

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