Question

10-15 pls

010 10.0 points A sinusoidal transverse wave travels along a wire of linear density 8.34 g/m. The wave has amplitude 1.2 cm, frequency 132 Hz and wavelength 3.07 m What is the tension of the wire? Answer in units of N 011 (part 1 of 2) 10.0 points A standing wave is formed on a string that is 32 m long, has a mass per unit length 0.00512 kg/m, and is stretched to a tension of 18 N Find the fundamental frequency Answer in units of cycles/s. 012 (part 2 of 2) 10.0 points Find the next frequency that could cause a standing wave pattern Answer in units of cycles/s. 013 10.0 points A student wants to establish a standing wave on a wire 2.5 m long clamped at both ends. The wave speed is 392 m/s. What is the minimum frequency she should apply to set up standing waves? Answer in units of Hz 014 (part 1 of 2) 10.0 points The length of a string is 1314 cm. It is held fixed at each end. The string vibrates in nine sections: i.e., the string has nine antinodes, and the string vibrates at 140 Hz Find the wavelength. Answer in units of m. 015 (part 2 of 2) 10.0 points What is the fundamental frequency? Answer in units of Hz.

Answer 1

10)

Velocity of transverse wave , $v=f\lambda$

Velocity of transverse waves v = squareroot t/u, v = f lambda squareroot t/u = f lambda t = f^2 lambda^2 u = (132)^2 (3.07)^2(8.34 * 10^-3) = 1370n tension in the wire is t = 1370n for a standing wave, fundamental frequency is f = v/2l = 1/2l squareroot t/u f = 1/2*32 squareroot 18/0.00512 = 0.926cycles/s f_1 = 2 v/2l = 2 1/2l squareroot t/u = 2 * 1/2*32 squareroot 18/0.00512 = 1.852 cycles/s minimum frequency to set up standing wave is fundamental frequency f = v/2l f = 392/2*2.5 = 78.4hz wave length of string is 9lambfda/2 and length of string is l = 1314cm 9 lambda/2 = l lambda = 2l/9 = 2*1314/9 = 292cm frequency of wave with nine sections as shown in figure is f� = 9 v/2l = 140hz implies v/2l = 15.6hz fundamental frequency of wave is f = v/2l = 15.6hz

$\sqrt{\frac{T}{\mu}}=f\lambda$

$T=f^2\lambda^2\mu=(132)^2(3.07)^2(8.34*10^{-3})=1370\,N$

Tension in the wire is $T=1370\,N$

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11)

For a standing wave, fundamental frequency is $f=\frac{v}{2L}=\frac{1}{2L}\sqrt{\frac{T}{\mu}}$

$f=\frac{1}{2*32}\sqrt{\frac{18}{0.00512}}=0.926\,cycles/s$

12) Next frequency is $f_1=2\frac{v}{2L}=2\frac{1}{2L}\sqrt{\frac{T}{\mu}}=2*\frac{1}{2*32}\sqrt{\frac{18}{0.00512}}=1.852\,cycles/s$

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13) Minimum frequency to set up standing wave is fundamental frequency , $f=\frac{v}{2L}$

$f=\frac{392}{2*2.5}=78.4\,Hz$

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14) Wavelength of string is $\frac{9\lambda}{2}$ and length of string is $L=1314\,cm$

$\frac{9\lambda}{2}=L$

$\lambda=\frac{2L}{9}=\frac{2*1314}{9}=292\,cm$

15) Frequency of wave with nine sections as shown in figure is $f'=9\frac{v}{2L}=140\,Hz$

$\Rightarrow$    $\frac{v}{2L}=15.6\,Hz$

Fundamental frequency of wave is $f=\frac{v}{2L}=15.6\,Hz$

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