Question

The frequency, f, of the nth note above a440, in hertz (hz), is given by the equation f (n) = 440 ⋅ 2ⁿ. What is the frequency of the 4th note above a440?

1) 880 Hz
2) 1760 Hz
3) 3520 Hz
4) 7040 Hz

Answer 1

To find the frequency of the 4th note above A440, we apply the formula f(n) = 440 ⋅ 2^n with n as 4, resulting in a calculated frequency of 7040 Hz.

The correct option is 4).

Step-by-step explanation:

To calculate the frequency of the 4th note above A440 using the given formula f(n) = 440 ⋅ 2^n, we simply need to input the value for n, which in this case is 4. Using this formula, the frequency of the 4th note above A440 is calculated as follows:

1. Replace n with 4 in the formula: f(4) = 440 ⋅ 2^4.
2. Calculate the power of 2 raised to 4: 2^4 = 16.
3. Multiply 440 Hz by 16: 440 Hz ⋅ 16 = 7040 Hz.

Therefore, the frequency of the 4th note above A440 is 7040 Hz, which corresponds with option 4.