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 ropes. A transverse pulse of wavelength \(\lambda_1\) is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is \(\lambda_2\). The ratio \(\dfrac{\lambda_2}{\lambda_1}\) is:
1. \(\sqrt{\dfrac{m_1+m_2}{m_1}}\)
2. \(\sqrt{\dfrac{m_2}{m_1}}\)
3. \(\sqrt{\dfrac{m_1+m_2}{m_2}}\)
4. \(\sqrt{\dfrac{m_1}{m_2}}\)
If n1, n2 and n3 are, are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by
1. 1/n=1/n1+1/n2+1/n3
2. 1/√n=1/√n1+1/√n2+1/√n3
3. √n=√n1+√n2+√n3
4. n=n1+n2+n3
When a string is divided into three segments of lengths the fundamental frequencies of these three segments are respectively. The original fundamental frequency (v) of the string is
1.
2.
3.
4.
A wave in a string has an amplitude of 2 cm. The wave travels in the +ve direction of x-axis with a speed of and it is noted that 5 complete waves fit in 4 m length of the string. The equation describing the wave is :
1.
2.
3.
4.
The equation of a wave traveling in a string can be written as . Its wavelength is :
(1) 100 cm
(2) 2 cm
(3) 5 cm
(4) None of the above