The stationary wave $y=2a\sin kx\cos \omega t$ in a closed organ pipe is the result of the superposition of $y=a\sin (\omega t-kx)$ and

(1) $y=-a\cos (\omega t+kx)$

(2) $y=-a\sin (\omega t+kx)$

(3) $y=a\sin (\omega t+kx)$

(4) $y=a\cos (\omega t+kx)$

An open pipe of length l vibrates in the fundamental mode. The pressure variation is maximum at :

(1) l/4 from ends

(2) The middle of the pipe

(3) The ends of the pipe

(4) At l/8 from ends of pipe

The fundamental frequency of pipe is 100 Hz and the other two frequencies are 300 Hz and 500 Hz then :

(1) The pipe is open at both the ends

(2) The pipe is closed at both the ends

(3) One end open and another end is closed

(4) None of the above

The fundamental frequency of an open pipe of length 0.5 m is equal to the frequency of the first overtone of a closed pipe of length l. The value of l_c is (m) :

(1) 1.5

(2) 0.75

(3) 2

(4) 1

In a closed organ pipe, the frequency of the fundamental note is 50 Hz. The note of which of the following frequencies will not be emitted by it :

(1) 50 Hz

(2) 100 Hz

(3) 150 Hz

(4) None of the above

On producing the waves of frequency 1000 Hz in a Kundt's tube, the total distance between 6 successive nodes is 85 cm. Speed of sound in the gas filled in the tube is 

(1) 330 m/s

(2) 340 m/s

(3) 350 m/s

(4) 300 m/s

What is the base frequency if a pipe gives notes of frequencies 425, 255 and 595 and decide whether it is closed at one end or open at both ends :

(1) 17, closed

(2) 85, closed

(3) 17, open

(4) 85, open

A student determines the velocity of sound with the help of a closed organ pipe. If the observed length for fundamental frequency is \(24.7~\text{cm}\), the length for third harmonic will be:
1. \(74.1~\text{cm}\)
2. \(72.7~\text{cm}\)
3. \(75.4~\text{cm}\)
4. \(73.1~\text{cm}\)

In a resonance tube the first resonance with a tuning fork occurs at 16 cm and second at 49 cm. If the velocity of sound is 330 m/s, the frequency of tuning fork is :

(1) 500

(2) 300

(3) 330

(4) 165

Two closed organ pipes of length 100 cm and 101 cm 16 beats in 20 sec. When each pipe is sounded in its fundamental mode calculate the velocity of sound 

(1) 303 ms^–1

(2) 332 ms^–1

(3) 323.2 ms^–1

(4) 300 ms^–1