Answer
$440$ vibrations per second.
Work Step by Step
Step 1:- Translate the statement to form an equation.
Let the pitch be $P$.
and the wavelength be $W$.
Because the pitch varies inversely as $W$, we have:
$\Rightarrow P=\frac{k}{W}$ ...... (1)
Step 2:- Substitute the first set of values into the equation to find the value of $k$.
The given values are $P=\$660$ vibrations per second and $W=1.6$ feet.
Substitute into the equation (1).
$\Rightarrow 660=\frac{k}{1.6}$
Multiply both sides by $1.6$.
$\Rightarrow 1.6\cdot 660=1.6\cdot \frac{k}{1.6}$
Simplify.
$\Rightarrow 1056=k$
Step 3:- Substitute the value of $k$ into the original equation.
Substitute $k=1056$ into the equation (1).
$\Rightarrow P=\frac{1056}{W}$ ...... (2)
Step 4:- Solve the equation to find the required value.
Substitute $W=2.4$ feet into the equation (2).
$\Rightarrow P=\frac{1056}{2.4}$
Simplify.
$\Rightarrow P=440$
Hence, the pitch of a tone is $440$ vibrations per second.
