Problem 14 - An Introduction to Physical Science

Question

Choose the word or phrase that best answers the question. When tuning a violin, a string is tightened. What happens to a note being played on the string? A) Its pitch is higher. B) Its pitch is lower. C) It is quieter. D) It is louder.

Step-by-Step Solution

Answer

A) Its pitch is higher.

Step 1 - Understand the Basics of Pitch

Pitch refers to how high or low a note sounds. It is determined by the frequency of the sound wave produced by the vibrating string.

Step 2 - Effect of Tightening a String

When a string is tightened, its tension increases. Increased tension results in a higher frequency of vibration.

Step 3 - Relate Frequency to Pitch

A higher frequency of vibration corresponds to a higher pitch. Therefore, tightening the string will raise the pitch of the note.

Step 4 - Choose the Correct Answer

Given the understanding that tightening a string raises the pitch, the best answer is A) Its pitch is higher.

Key Concepts

pitch

Pitch is an essential concept in music and acoustics, describing how high or low a note sounds. It is closely related to the frequency of the sound wave produced by the object creating the sound. Higher frequencies correspond to higher pitches, while lower frequencies correspond to lower pitches.
When you play an instrument like the violin, you adjust the pitch by changing the tension, length, or mass of the vibrating string. For instance, tightening a violin string increases its tension, which as we'll see, affects its frequency and thus its pitch.

frequency

Frequency, which is measured in Hertz (Hz), is the number of times a string vibrates per second. This is a fundamental property in understanding how musical instruments work. The frequency of a violin string determines its pitch:

• If the frequency is high, the pitch is high—imagine the sharp sound of a high-pitched note.
• If the frequency is low, the pitch is low—think of the deep sound of a low-pitched note.

When you tighten a violin string, you increase its frequency. The increased tension makes the string vibrate faster, leading to a higher note.
Mathematically, the relationship is given by:
\[ f = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \]
where:
\( f \) is the frequency, \( L \) is the length of the string, \( T \) is the tension, and \( \mu \) is the linear density of the string (mass per unit length).

vibrating string

A vibrating string on a violin produces sound waves that we perceive as musical notes. Various factors influence how a string vibrates:

• Tension: Tightening a string increases its tension, leading to higher frequencies and pitches.
• Length: Shortening the effective length of the string (like pressing down on the fingerboard) increases frequency and pitch.
• Mass: Heavier strings vibrate slower, producing lower frequencies and pitches.

When a string is tightened, its tension increases. This higher tension forces the string to vibrate more rapidly, raising the frequency and, consequently, the pitch. Therefore, the pitch of the note you hear on a tightened violin string will be higher. This explains why the correct answer to the exercise question is that tightening the string raises the pitch of the note (Answer A).