Discover new information and insights with the help of IDNLearn.com. Our Q&A platform offers reliable and thorough answers to help you make informed decisions quickly and easily.

A sound wave generated by a musical note has the characteristics presented in the table. What is the missing value?

\begin{tabular}{|c|c|c|c|}
\hline
Medium & \begin{tabular}{c}
Wave speed \\
[tex]$( m / s )$[/tex]
\end{tabular} & \begin{tabular}{c}
Frequency \\
[tex]$( Hz )$[/tex]
\end{tabular} & \begin{tabular}{c}
Wavelength \\
[tex]$( m )$[/tex]
\end{tabular} \\
\hline
Air & 346 & 55 & 6.3 \\
\hline
Glass & 5,640 & 55 & 102 \\
\hline
Brass & 4,700 & 55 & [tex]$?$[/tex] \\
\hline
\end{tabular}

A. 85
B. 98
C. 100
D. 112


Sagot :

To determine the missing wavelength value in brass when given the wave speed and frequency, we can use the relationship between wave speed, frequency, and wavelength. The formula that connects these quantities is:

[tex]\[ v = f \times \lambda \][/tex]

where:
- [tex]\( v \)[/tex] is the wave speed,
- [tex]\( f \)[/tex] is the frequency, and
- [tex]\( \lambda \)[/tex] is the wavelength.

Given values for brass:
- Wave speed [tex]\( v = 4700 \, \text{m/s} \)[/tex]
- Frequency [tex]\( f = 55 \, \text{Hz} \)[/tex]

We need to find the wavelength [tex]\( \lambda \)[/tex]. We can rearrange the formula to solve for wavelength:

[tex]\[ \lambda = \frac{v}{f} \][/tex]

Substitute the given values into the equation:

[tex]\[ \lambda = \frac{4700 \, \text{m/s}}{55 \, \text{Hz}} \][/tex]

Carrying out the division:

[tex]\[ \lambda \approx 85.45454545454545 \, \text{m} \][/tex]

Given the options:
A. 85
B. 98
C. 100
D. 112

The closest value to our calculated wavelength [tex]\( 85.45454545454545 \, \text{m} \)[/tex] is:

A. 85.

Thus, the missing wavelength value for brass is 85 meters.