A pipe open at both ends has a fundamental frequency \(f\) in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to:

The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is

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

In a guitar, two strings \(A\) and \(B\) made of same material are slightly out of tune and produce beats of frequency \(6\,Hz\). When tension in \(B\) is slightly decreased, the beat frequency increases to \(7\,Hz\). If the frequency of \(A\) is \(530\,Hz\), the original frequency of \(B\) will be

A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of \(27^\circ C\) two successive resonances are produced at \(20\,cm\) and \(73\,cm\) of column length. If the frequency of the tuning fork is \(320\,Hz\), the velocity of sound in air at \(27^\circ C\) is

The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is \(20\,cm\), the length of the open organ pipe is

The two nearest harmonics of a tube closed at one end and open at other end are \(220\, Hz\) and \(260\, Hz\). What is the fundamental frequency of the system?

Two cars moving in opposite directions approach each other with speed of \(22\,ms^{−1}\) and \(16.5\,ms^{−1}\) 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 is \(340\,ms^{−1}\)]

A siren emitting a sound of frequency \(800\, Hz\) moves away from an observer towards a cliff at a speed of \(15\, \text{ms}^{−1}\). Then, the frequency of sound that the observer hears in the echo reflected from the cliff is (Take velocity of sound in air = \(330\,\text{ms}^{−1}\))

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 \(50\, \text{Cm}\). The next larger length of the column resonating with the same tuning fork is

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 when it reaches the top of the rope is \(λ_2\).The ratio \(\displaystyle \frac{λ_1}{λ_2}\) is