Two blocks each having a mass of 3.2 kg are connected by a wire CD and the system is suspended from the ceiling by another wire AB as shown in the figure. The linear mass density of the wire AB is 10 g/m and that of CD is 8 g/m. Find the speed of a transverse wave pulse produced in AB and in CD.
$$m_1 = m_2 = 3.2 kg$$
mass per unit length of $$AB = 10 g/mt = 0.01 kg.mt$$
mass per unit length of $$CD = 8 g/mt = 0.008 kg/mt$$
for the string $$CD, T = 3.2 \times g$$
$$\Rightarrow v= \sqrt{(T/m)} = \sqrt{(3.2 \times 10)/0.008} = \sqrt{(32 \times 10^3)/8} = 2 \times 10\sqrt{10} = 20 \times 3.14 = 63 m/s$$
for the string $$AB, T = 2 \times 3.2 g = 6.4 \times g = 64 N$$
$$\Rightarrow v = \sqrt{(T/ m)} = \sqrt{(64/0.01)} = \sqrt{6400} = 80 m/s$$
Speed of a transverse wave on a straight wire (mass $$6.0\ g$$, length $$60$$ cm) and area of cross-section ($$1.0\ mm^2$$) is $$90\,ms^{-1}$$. If the Young's modulus of wire is $$16\times 10^{11}Nm^{-2}$$, the extension of wire over its natural length is :
Equation of travelling wave on a stretched string of linear density $$5 g/m$$ is $$y = 0.03 sin(450 t 9x)$$ where distance and time are measured is SI units. The tension in the string is :
The equation of a wave on a string of linear mass density $$0.04 kg \mathrm{m}^{-1}$$ is given by $$\displaystyle \mathrm{y}=0.02(\mathrm{m})\sin\left [2\pi \left (\dfrac{\mathrm{t}}{0.04(\mathrm{s})}-\dfrac{\mathrm{x}}{0.50(\mathrm{m})}\right)\right]$$. The tension in the string 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 $${\lambda}_{1}$$ 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 $${{\lambda}_{2}}/{{\lambda}_{1}}$$ is:
A uniform string is vibrating with a fundamental frequency '$$f$$'. The new frequency, if radius and length both are doubted would be:
A string wave equation is given $$y = 0.002\sin (300t - 15x)$$ and mass density is $$\left (\mu = \dfrac {0.1\ kg}{m}\right )$$. Then find the tension in the string.
A transverse wave is propagating on the string. The linear density of a vibrating string is $$10^{-3}$$ kg/m. The equation of the wave is $$Y=0.05\sin(x+15t)$$ where x and Y are in metre and time in second. The tension in the string is?
Two strings A and B, made of same material, are stretched by the same tension. The radius of string A is double of radius of B. A transverse wave travel on A with speed $$v_A $$ and B with speed $$v_B $$. The ratio $$v_A/v_B $$ is
Two wires of different densities but same area of cross-section are soldered together at one end and are stretched to a tension T. The velocity of a transverse wave in the first wire is double of that in the second wire. Find the ratio of the density of the first wire to that of the second wire.
A steel wire of length $$64\ cm$$ weighs $$5\ g$$. If it is stretched by a force of $$8\ N$$, what would be the speed of a transverse wave passing on it?