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Chapter 16: Q39P (page 474)

Two sinusoidal waves of the same period, with amplitudes of 5.0and 7.0 mm, travel in the same direction along a stretched string; they produce a resultant wave with an amplitude of 9.0 mm. The phase constant of the 5.0 mmwave is 0.What is the phase constant of the 7.0 mmwave?

Short Answer

Expert verified

Phase constant of the 7 mm wave is84掳

Step by step solution

01

The given data

i) Amplitudes of two waves, ym1=5.0mmandym2=7.0mm

ii) Amplitude of resultant wave, ym=9.0mm

iii) Phase constant of 5.00 mm wave, 胃=0掳

02

Understanding the concept of phase

The phase constant of sinusoidal waves of the same period which travel in the same direction is given by the cosine formula, and it can be shown in a phase diagram.

Formula:

Phase constant using Cosine Formula,

ym2=ym12+ym22-2ym1ym2肠辞蝉胃=ym12+ym22-2ym1ym2cos蠁 (i)

03

Calculation of phase of 7.00 mm wave

Phasor diagram can be drawn as below:

As we need to find the phase constant i.e. 蠁Hence, using equation (i) and given values, we get the value of phase as:

cos蠁=ym2-ym12+ym222ym1ym2cos蠁=9.02-5.02+7.0225.07.0cos蠁=0.10蠁=84掳

Hence, the value of phase is84掳

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Most popular questions from this chapter

A transverse sinusoidal wave is moving along string in the positive direction of an xaxis with a speed of 80 m/s. At t = 0, the string particle atx = 0 has a transverse displacement of 4.0 cmfrom its equilibrium position and is not moving. The maximum transverse speed of the string particle at x = 0is 16 m/s. (a)What is the frequency of the wave? (b)What is the wavelength of the wave?If y(x,t)=ymsin(kx卤蝇t+蠒)is the form of the wave equation, (a)What isym, (b)What is k, (c)What is 蝇, (d)What is, and (e)What is the correct choice of sign in front of蝇?

A generator at one end of a very long string creates a wave given by

y1=(6.0cm)cos蟺2[2.00m-1x+8.00s-1t]

and a generator at the other end creates the wave

y2=(6.0cm)cos蟺2[(2.00m-1)x-(8.00s-1)t]

Calculate the (a) frequency, (b) wavelength, and (c) speed of each wave.

For x鈮�0, what is the location of the node having the (d) smallest, (e) second smallest, and (f) third smallest value of x? Forx鈮�0, what is the location of the antinode having the (g) smallest, (h) second smallest, and (i) third smallest value ofx?

A traveling wave on a string is described by

y=2.0sin[2蟺t0.40+x80]

Where and are in centimeters and tis in seconds. (a) For t = 0, plot yas a function of xfor0鈮�x鈮�160cm. (b) Repeat (a) for t = 0.05s andt = 0.10s.From your graphs, determine (c) the wave speed and (d) thedirection in which the wave is traveling.

What phase difference between two identical traveling waves, moving in the same direction along a stretched string, results in the combined wave having an amplitude1.50 times that of the common amplitude of the two combining waves? (a)Express your answer in degrees, (b) Express your answer in radians, and (c) Express your answer in wavelengths.

A sinusoidal wave is sent along a cord under tension, transporting energy at the average rate ofPavg1,1.Two waves, identical to that first one, are then to be sent along the cord with a phase difference 蠁of either0,0.2 wavelength, or 0.5wavelength. (a) With only mental calculation, rank those choices of蠁according to the average rate at which the waves will transport energy, greatest first. (b) For

The first choice of蠁, what is the average rate in terms oflocalid="1661229908063" Pavg1?
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