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dusya [7]
3 years ago
10

A plucked violin string carries a traveling wave given by the equation f(x,t)=asin[b(x−ct)+ϕi], with a = 0.00580 m , b = 33.05 m

−1 , and c = 245 m/s .
A) If f(0, 0) = 0, what is ϕi?

B) Determine the simple harmonic period of a point on the string.
Physics
2 answers:
Viktor [21]3 years ago
0 0

Answer:

A) Φ = 0 , B)  T = 7.76 s

Explanation:

A) to find the value of the phase constant replace the value

          0 = a sin (b (0- 0) + Φ)

           0 = sin Φ

           Φ = sin⁻¹ 0

           Φ = 0

B) the period is defined by time or when the movement begins to repeat itself

So that the sine function is repeated when the angle passes 2pi

            b (x- ct) = 2pi

If we are at a fixed point x = 0

           b c t = 2pi

            t = 2π / bc

Let's calculate

            T = 2π / (33.05 245)

            T = 7.76 s

ratelena [41]3 years ago
0 0

Answer:

A. Φi = 0

B. Simple harmonic period, T = 0.0445s

Explanation:

Parameters given:

a = 0.00580 m

b = 33.05 m-1

c = 245 m/s

A. At time t = 0 and point x = 0, f(x, t) = 0. Hence, the string is not moving at all. It is static and in its start position.

f(x, t) = asin[b(x - ct) + Φi]

f(0,0) = asin[b(0 - 0) + Φi] = 0

asin[b(0) - Φi] = 0

asin[Φi] = 0

sinΦi = 0

Φi = sin-1(0)

Φi = 0

B. By comparing the given function with the general wave function,

f(x, t) = Asin(kx - ωt + Φ)  ;  f(x, t) = asin(bx - bct + Φi)

a = A (amplitude of the wave)

b = k (wave number)

bc = ω (angular frequency)

The period of the simple harmonic motion can then be found using:

T = 2π/ω

=> T = 2π/bc

T = 2π/(33×245)

T = 0.0445 s

The simple harmonic period is 0.0445s

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The heat energy required to melt 0.05 kg of aluminum is obtained from the heat capacity of aluminum and the melting point of aluminum.

The formula to be used is given below:

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Answer:

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r=\frac{d}{2}\\\Rightarrow r=\frac{2.39}{2}\\\Rightarrow r=1.195\ m

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T=\frac{t}{N}\\\Rightarrow T=\frac{22.7}{8}\\\Rightarrow T=2.8375\ s

Time period of the motion is 2.8375 s

Angular speed is given by

\omega=\frac{2\pi}{T}\\\Rightarrow \omega=\frac{2\pi}{2.8375}\\\Rightarrow \omega=2.21433\ rad/s

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