1. A transverse wave moves along a rope. A point on the medium carrying the wave is observed. A graph of displacement versus time of the point is shown below. The vertical distance between a crest and a trough is $$ 2,4 \mathrm{~cm} $$. 11.1 How many completed waves are there between $$ \mathrm{t}=0 \mathrm{~s} $$ to $$ \mathrm{t}=0,15 \mathrm{~s} $$ ? $$ \qquad $$ 11.2 From the given information, write down the amplitude of the wave. $$ \qquad $$ 11.3 Calculate the period of the wave. $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ 14. The wave motion takes 10 s to complete one vibration. 14.1 How long did it take 8 waves to move past a certain point? $$ \qquad $$ $$ \qquad $$ 14.2 What is the period of the wave motion? $$ \qquad $$ 14.4 Calculate the frequency of the wave series. $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ 14.3 Calculate the wavelength of the wave series. $$ \qquad $$ $$ \qquad $$ 14.5 Calculate the speed of the wave series. $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ WAVES, SOUND AND LIGHT 176

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UpStudy AI · Accepted Answer

Sure, let's tackle each part of your questions step by step. Some parts require specific information (like the graph mentioned in Problem 11.1), which isn't provided, so I'll address those accordingly.

---

### **Problem 11**

**Given:**
- The vertical distance between a crest and a trough is $$ 2.4 $$ cm.

#### **11.1 How many completed waves are there between $$ t = 0 $$ s to $$ t = 0.15 $$ s?**

**Answer:**
To determine the number of completed waves in a given time interval, we need to know the **period (T)** of the wave, which is the time it takes to complete one full cycle. The period can be derived from the graph of displacement versus time by measuring the time between successive crests or troughs.

- **However**, since the graph is not provided, **we cannot determine the number of completed waves** between $$ t = 0 $$ s and $$ t = 0.15 $$ s without additional information about the wave's period or frequency.

---

#### **11.2 From the given information, write down the amplitude of the wave.**

**Answer:**
The **amplitude (A)** of a wave is the maximum displacement from the equilibrium position. Given the vertical distance between a crest and a trough is $$ 2.4 $$ cm, the amplitude is half of this value.

$$
A = \frac{\text{Distance between crest and trough}}{2} = \frac{2.4\, \text{cm}}{2} = 1.2\, \text{cm}
$$

**So, the amplitude of the wave is $$ 1.2 $$ cm.**

---

#### **11.3 Calculate the period of the wave.**

**Answer:**
The **period (T)** is the time it takes to complete one full wave cycle. To calculate the period, you'd typically use the time interval over which a certain number of waves pass a point.

$$
T = \frac{\text{Total Time}}{\text{Number of Waves}}
$$

- **However**, without knowing either the period directly from the graph or the number of waves that occur in $$ 0.15 $$ seconds (from part 11.1), **we cannot calculate the period**.

---

### **Problem 14**

**Given:**
- The wave motion takes $$ 10 $$ seconds to complete one vibration.

#### **14.1 How long did it take 8 waves to move past a certain point?**

**Answer:**
The time taken for multiple waves can be calculated by multiplying the period by the number of waves.

$$
\text{Time for 8 waves} = \text{Number of Waves} \times \text{Period} = 8 \times 10\, \text{s} = 80\, \text{s}
$$

**So, it took $$ 80 $$ seconds for 8 waves to move past the point.**

---

#### **14.2 What is the period of the wave motion?**

**Answer:**
The **period (T)** is the time taken to complete one full wave.

$$
T = 10\, \text{seconds}
$$

**So, the period of the wave motion is $$ 10 $$ seconds.**

---

#### **14.3 Calculate the wavelength of the wave series.**

**Answer:**
The **wavelength ($$ \lambda $$)** is the distance between successive crests (or troughs) of the wave. To calculate the wavelength, you need to know the **wave speed (v)** or have additional information relating speed, frequency, and wavelength.

The relationship between wave speed, frequency, and wavelength is:

$$
v = f \times \lambda
$$

Where:
- $$ v $$ = Wave speed
- $$ f $$ = Frequency
- $$ \lambda $$ = Wavelength

**Given:**
- Period $$ T = 10 $$ s
- Frequency $$ f = \frac{1}{T} = \frac{1}{10\, \text{s}} = 0.1\, \text{Hz} $$

**However, without the wave speed $$ v $$, we cannot calculate the wavelength $$ \lambda $$.**

---

#### **14.4 Calculate the frequency of the wave series.**

**Answer:**
Frequency ($$ f $$) is the number of waves that pass a point per unit time. It's the reciprocal of the period.

$$
f = \frac{1}{T} = \frac{1}{10\, \text{s}} = 0.1\, \text{Hz}
$$

**So, the frequency of the wave series is $$ 0.1 $$ Hz.**

---

#### **14.5 Calculate the speed of the wave series.**

**Answer:**
To calculate the **wave speed ($$ v $$)**, use the relationship:

$$
v = f \times \lambda
$$

**Given:**
- Frequency $$ f = 0.1\, \text{Hz} $$
- Wavelength $$ \lambda $$ = ?

**However, since the wavelength $$ \lambda $$ is not provided or cannot be determined from the given information, we **cannot calculate the wave speed** numerically.

**If $$ \lambda $$ were known, you would plug in the values as follows:**

$$
v = 0.1\, \text{Hz} \times \lambda
$$

---

### **Summary of Answers**

- **11.1:** Cannot determine without the graph or additional information.
- **11.2:** Amplitude $$ A = 1.2 $$ cm.
- **11.3:** Cannot calculate without knowing the period or frequency.
- **14.1:** $$ 80 $$ seconds.
- **14.2:** $$ 10 $$ seconds.
- **14.3:** Cannot calculate without wave speed or wavelength.
- **14.4:** $$ 0.1 $$ Hz.
- **14.5:** Cannot calculate without knowing the wavelength.

If you have additional data or the graph mentioned in Problem 11, feel free to provide it, and I can help you further!
Cannot determine the number of completed waves without additional information. The amplitude is 1.2 cm. Cannot calculate the period without more data. It took 80 seconds for 8 waves to pass a point. The period is 10 seconds. Cannot calculate the wavelength without wave speed or additional information. The frequency is 0.1 Hz. Cannot calculate the wave speed without knowing the wavelength.

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