a transverse wave on a string has a period of 0.1 s and an amplitude of 1 cm. What is the
maximum transverse acceleration at any point along the string?
To find the maximum transverse acceleration at any point along the string, we need to use the formula for transverse acceleration in a wave. The formula is:
a = 4π²f²A
Where:
a is the transverse acceleration,
π is approximately 3.14159,
f is the frequency of the wave,
and A is the amplitude of the wave.
In this case, we are given the period of the wave instead of the frequency. The relationship between period (T) and frequency (f) is:
T = 1/f
So, we can rewrite the formula for transverse acceleration as:
a = 4π²(1/T)²A
Now, let's substitute the given values into the formula:
T = 0.1 s (period)
A = 1 cm = 0.01 m (amplitude)
Plugging these values into the formula, we get:
a = 4π²(1/0.1)²(0.01)
Simplifying this equation, we calculate:
a = 4π²(10)²(0.01)
a = 4π²(100)(0.01)
a = 4π²
Now we can evaluate this expression:
a ≈ 39.48 m/s²
Therefore, the maximum transverse acceleration at any point along the string is approximately 39.48 m/s².