Question

Write an equation for the position of the cart as a function of time using the given quantities above.b) Write an equation for the frequency heard by a stationary observer standing to the right of the track as a function of time.c) If the maximum sound level heard by the person is 75 decibels when the speaker is at its closest distance 1.00 m from him, what is the minimum sound level heard by the observer in decibels

Answer 1

(a). w/ 2π = 1/2π × (√k + ky/m).

(b). Vi/( Vi + Aw sin wt) or Vi/( Vi - Aw sin wt).

(c). 68.97 dB.

Step-by-step explanation:

We are given that the two springs constant = k and ky respectively, mass = m.

So, k which is the left hand spring is stretched to the right and ky which is the right hand spring is stretched to the left. Thus, we will have;

Total force = - (k + ky) ∆x. Where ∆x = displacement.

So, total force = displacement.

Thus, mw^2 ∆x = (k + ky) ∆x.

w^2 = (k + ky)/ m.

Therefore, the frequency,

= w/ 2π = 1/2π × (√k + ky/m).

(b). In simple harmonic motion, the displacement, x(t) = A cos(wt).

Therefore, the velocity = dx(t)/ dt = - Aw sin wt.

Hence, the frequency heard:

= Vi/( Vi + Aw sin wt) or Vi/( Vi - Aw sin wt).

(C). Minimum intensity = (4π × maximum intensity)/ 4π × (2)^2.

= Maximum intensity/ 4.

Hence, the intensity level, y = 10 log I(min)/ I(h).

= 10 log (0.79 × 10^7).

= 68.97 dB.