Physics: speed of wave along a string

[sunsfan]

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Consider 2 strings of the same material. The strings are fixed at both ends. Waves are generated along these strings by a 60 cycles/sec vibrator as shown.
Fig 1 shows a sinusoidal wave with amplitude = 3 mm, wavelength = 2 cm
Fig 2 shows a sinusoidal wave with amplitude = 6 mm, wavelength = 4 cm

Compare the speed of the wave on String 1 to the speed of wave on String 2.
A. Wave 1 is twice as fast as Wave 2
B. Wave 2 is twice as fast as Wave 1
C. The wave speeds are equal
D. There is no way to determine wave speeds.

The correct answer is B. Why not C??? 🙁

 

[161927]

Consider 2 strings of the same material. The strings are fixed at both ends. Waves are generated along these strings by a 60 cycles/sec vibrator as shown.
Fig 1 shows a sinusoidal wave with amplitude = 3 mm, wavelength = 2 cm
Fig 2 shows a sinusoidal wave with amplitude = 6 mm, wavelength = 4 cm

Compare the speed of the wave on String 1 to the speed of wave on String 2.
A. Wave 1 is twice as fast as Wave 2
B. Wave 2 is twice as fast as Wave 1
C. The wave speeds are equal
D. There is no way to determine wave speeds.

The correct answer is B. Why not C??? 🙁

v=fw, constant frequency, if wavelength increases by a factor 2 then v increases linearly

 

[sunsfan]

But isn't the speed of a wave determined only by the properties of the medium: its elastic factor and inertial factor?
For example, a wave traveling along a string has
v=(T/"mu")^0.5
where v = wave speed
T = tension in string
"mu" = mass per unit length of string

I'm still confused. 😕

 

[not respect]

you are way overthinking it, velocity = wavelength * frequency, the bulk properties are DIFFERENT and that's why the wavelengths in the problem are different.

 

[sunsfan]

you are way overthinking it, velocity = wavelength * frequency, the bulk properties are DIFFERENT and that's why the wavelengths in the problem are different.

By that, do you mean the intensive properties of the strings in the 2 scenarios are different? How can that be when it's stated in the passage that the strings are made of the same material?

Oh wait.... are you saying that the fact that the identical vibrators shaking strings of identical material produced waves of different amplitudes and wavelengths must mean that the tension in the strings are different to begin with? And if the tensions are different, then the speeds will definitely not be the same? Am I finally getting this? (excited anticipation) 😱

 

[wrathofgod64]

I think ur getting it. One way to solve it using your formula, although much longer, is this.

Wave 1:
60 = n1*sqrt(F1/u)/2L

Wave 2:
60 = n2*sqrt(F2/u)/2L

and λ = 2L/n

You should discover using these equations that n1=2*n2 and that F1=4*Fu, making the wave velocity for wave 2 is twice that of wave 1. So you're right, the tension on wave 2 is 4x the tension on wave 1, which is the only way the wave speeds could be different, since they're the same material.

 

[sunsfan]

I think ur getting it. One way to solve it using your formula, although much longer, is this.

Wave 1:
60 = n1*sqrt(F1/u)/2L

Wave 2:
60 = n2*sqrt(F2/u)/2L

and λ = 2L/n

You should discover using these equations that n1=2*n2 and that F1=4*Fu, making the wave velocity for wave 2 is twice that of wave 1. So you're right, the tension on wave 2 is 4x the tension on wave 1, which is the only way the wave speeds could be different, since they're the same material.

Yesssss!
You are awesome. Thanks.